I think you may be confusing "skinheads" with "racist skinheads." It is important to realize that the origins of the skinhead movement in the 60's were inherently anti-racist and were actually in large part the expression of an English mod imitation/celebration of Jamaican rude boy culture. That is largely the case today; I was involved in the punk scene in the Northeastern United States for a time, and every skin I met, save one, was a supporter of a leftist skin group like SHARP or Anti-Racist Action. The lone exception was a guy who had become a skin after going to prison and subsequently joining a white power group.

That said - while perhaps there were pre-NSDAP individuals or groups that shaved their heads, I don't know of any organization that used shaved heads as their chief identifier, although I anticipate that's not really what you're asking here. An important thing to remember as far as the history of shaven heads is concerned is that until the advent of the electric razor shortly before WWII, it was laborious and time-consuming to shave one's head bald, and nearly impossible to trim a head of hair into the uniform buzz-cut that we associate with early skins.

/u/OneMoGin answer is great, but should insist more on one point: the Skinhead movement emerged as a subculture in the UK in the late 60's. There were no skinheads before that.

I can't talk for the UK, but in France, the first groups of Skinheads (importing the culture from the UK) emerged in the late 70's, early 80's . While also apolitical at the beginning, they are rapidly taken over by the far right and as soon a the mid-80's, Skinhead is synonymous with fascist and racist in French media.

Before the Skinheads, a racist subculture existed in France and was called the Rebels. They had a classic rocker look and were displaying a confederate flag as patches on their jackets.

Source: this French documentary about the Antifascist movement in France : https://www.youtube.com/watch?v=boVr0SRS1Pw . [ jumb to 29:00 for the part about the Rebels ]